Import Andrew’s SPSS data

Map new names to variables.

Remove certain predictor variables:

• Clinical cutoffs
• Raw scores
• Total scores

##  [1] "ECBI_intensity_raw_score"       "ECBI_intensity_clinical_cutoff"
##  [3] "ECBI_problem_raw_score"         "ECBI_problem_clinical_cutoff"  
##  [5] "SEPTI_n_clinical_cutoff"        "SEPTI_d_clinical_cutoff"       
##  [7] "SEPTI_p_clinical_cutoff"        "SEPTI_r_clinical_cutoff"       
##  [9] "SEPTI_total"                    "SEPTI_total_clin_cutoff"

Build analysis data set. Exclude if missing any dependent variable, PCB1_Total, PCB2_Tot, PCB3_Total. Exclude rows if there are a high proportion of row-wise NA.

##    PCB1_Total       PCB2_Tot       PCB3_Total   
##  Min.   :18.00   Min.   : 6.00   Min.   :15.00  
##  1st Qu.:58.00   1st Qu.:22.00   1st Qu.:39.00  
##  Median :71.00   Median :25.00   Median :48.00  
##  Mean   :67.85   Mean   :24.53   Mean   :47.58  
##  3rd Qu.:81.00   3rd Qu.:28.00   3rd Qu.:57.00  
##  Max.   :90.00   Max.   :30.00   Max.   :75.00

https://uc-r.github.io/hc_clustering http://www.sthda.com/english/wiki/factoextra-r-package-easy-multivariate-data-analyses-and-elegant-visualization

## 
## To cite package 'factoextra' in publications use:
## 
##   Alboukadel Kassambara and Fabian Mundt (2017). factoextra:
##   Extract and Visualize the Results of Multivariate Data Analyses.
##   R package version 1.0.5.
##   https://CRAN.R-project.org/package=factoextra
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {factoextra: Extract and Visualize the Results of Multivariate Data Analyses},
##     author = {Alboukadel Kassambara and Fabian Mundt},
##     year = {2017},
##     note = {R package version 1.0.5},
##     url = {https://CRAN.R-project.org/package=factoextra},
##   }

## [1] 345  63

## [1] 345  54

## [1] 345   8

## [1] 345 154

## NULL

K-means clustering

## Clustering k = 1,2,..., K.max (= 10): .. done
## Bootstrapping, b = 1,2,..., B (= 500)  [one "." per sample]:
## ...................

## Warning: did not converge in 10 iterations

## ............................... 50 
## .................................................. 100 
## .................................................. 150 
## .................................................. 200 
## .................................................. 250 
## .................................................. 300 
## .................................................. 350 
## .................................................. 400 
## ......

## Warning: did not converge in 10 iterations

## ............................................ 450 
## .................................................. 500

## .
##   1   2   3 
##  97  41 207

## Within cluster sum of squares, cluster 1: 17104.40
## Within cluster sum of squares, cluster 2: 7267.38
## Within cluster sum of squares, cluster 3: 25793.53

## Between SS / Total SS: 2810.69 / 52976.00 = 5.31%

## Total within SS: 50165.31

Partitioning around medoids (PAM)

## Clustering k = 1,2,..., K.max (= 25): .. done
## Bootstrapping, b = 1,2,..., B (= 500)  [one "." per sample]:
## .................................................. 50 
## .................................................. 100 
## .................................................. 150 
## .................................................. 200 
## .................................................. 250 
## .................................................. 300 
## .................................................. 350 
## .................................................. 400 
## .................................................. 450 
## .................................................. 500

## .
##   1   2 
## 214 131

Agglomerative hierarchical clustering (AGNES)

Correlation between cophenetic distance and the original distance is 0.383.

The closer the value of the correlation coefficient is to 1, the more accurately the clustering solution reflects your data. Values above 0.75 are felt to be good.

Agglomerative coeffficient using the Ward method is 0.887.

k = 2 clusters

##   cluster size ave.sil.width
## 1       1  324          0.27
## 2       2   21          0.14

## .
##   1   2 
## 324  21

k = 3 clusters

##   cluster size ave.sil.width
## 1       1  190          0.08
## 2       2  134          0.03
## 3       3   21          0.12

## .
##   1   2   3 
## 190 134  21

k = 4 clusters

##   cluster size ave.sil.width
## 1       1  144          0.14
## 2       2  134         -0.01
## 3       3   46         -0.03
## 4       4   21          0.10

## .
##   1   2   3   4 
## 144 134  46  21

k = 5 clusters

##   cluster size ave.sil.width
## 1       1  144          0.09
## 2       2  106          0.02
## 3       3   46         -0.04
## 4       4   28          0.00
## 5       5   21          0.09

## .
##   1   2   3   4   5 
## 144 106  46  28  21

Divisive hierarchical clustering (DIANA)

Divisive coeffficient is 0.727.

k = 2 clusters

##   cluster size ave.sil.width
## 1       1  330          0.30
## 2       2   15          0.11

## .
##   1   2 
## 330  15

k = 3 clusters

##   cluster size ave.sil.width
## 1       1  329          0.30
## 2       2   15          0.11
## 3       3    1          0.00

## .
##   1   2   3 
## 329  15   1

k = 4 clusters

##   cluster size ave.sil.width
## 1       1  307          0.22
## 2       2   15          0.06
## 3       3   22          0.16
## 4       4    1          0.00

## .
##   1   2   3   4 
## 307  15  22   1

k = 5 clusters

##   cluster size ave.sil.width
## 1       1  289          0.20
## 2       2   18          0.05
## 3       3   15          0.05
## 4       4   22          0.15
## 5       5    1          0.00

## .
##   1   2   3   4   5 
## 289  18  15  22   1

Compare

Comparison between agnes and diana doesn’t give much insight.

Do not evaluate

Examine clusters

• k = 2 clusters seems optimal using AGNES
• k = 2 clusters seems optimal using DIANA

##    
##       1   2
##   1 316   8
##   2  14   7

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Final cluster identification

Use DIANA, k = 2

## .
##   1   2 
## 330  15

https://uc-r.github.io/hc_clustering http://www.sthda.com/english/wiki/factoextra-r-package-easy-multivariate-data-analyses-and-elegant-visualization

## 
## To cite package 'factoextra' in publications use:
## 
##   Alboukadel Kassambara and Fabian Mundt (2017). factoextra:
##   Extract and Visualize the Results of Multivariate Data Analyses.
##   R package version 1.0.5.
##   https://CRAN.R-project.org/package=factoextra
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {factoextra: Extract and Visualize the Results of Multivariate Data Analyses},
##     author = {Alboukadel Kassambara and Fabian Mundt},
##     year = {2017},
##     note = {R package version 1.0.5},
##     url = {https://CRAN.R-project.org/package=factoextra},
##   }

## [1] 345  63

## [1] 345  54

## [1] 345   6

## [1] 345   6

## NULL

K-means clustering

## Clustering k = 1,2,..., K.max (= 10): .. done
## Bootstrapping, b = 1,2,..., B (= 500)  [one "." per sample]:
## .................................................. 50 
## .................................................. 100 
## .................................................. 150 
## .................................................. 200 
## .................................................. 250 
## .................................................. 300 
## .................................................. 350 
## .................................................. 400 
## .................................................. 450 
## .................................................. 500

## .
##  1  2  3  4  5 
## 67 96 19 76 87

## Within cluster sum of squares, cluster 1: 232.49
## Within cluster sum of squares, cluster 2: 231.94
## Within cluster sum of squares, cluster 3: 72.29
## Within cluster sum of squares, cluster 4: 122.39
## Within cluster sum of squares, cluster 5: 237.95

## Between SS / Total SS: 1166.94 / 2064.00 = 56.54%

## Total within SS: 897.06

Partitioning around medoids (PAM)

## Clustering k = 1,2,..., K.max (= 10): .. done
## Bootstrapping, b = 1,2,..., B (= 500)  [one "." per sample]:
## .................................................. 50 
## .................................................. 100 
## .................................................. 150 
## .................................................. 200 
## .................................................. 250 
## .................................................. 300 
## .................................................. 350 
## .................................................. 400 
## .................................................. 450 
## .................................................. 500

## .
##   1   2 
## 193 152

Agglomerative hierarchical clustering (AGNES)

Correlation between cophenetic distance and the original distance is 0.565.

The closer the value of the correlation coefficient is to 1, the more accurately the clustering solution reflects your data. Values above 0.75 are felt to be good.

Agglomerative coeffficient using the Ward method is 0.980.

k = 2 clusters

##   cluster size ave.sil.width
## 1       1  265          0.39
## 2       2   80          0.25

## .
##   1   2 
## 265  80

k = 3 clusters

##   cluster size ave.sil.width
## 1       1  127          0.19
## 2       2  138          0.17
## 3       3   80          0.16

## .
##   1   2   3 
## 127 138  80

Divisive hierarchical clustering (DIANA)

Divisive coeffficient is 0.926.

k = 2 clusters

##   cluster size ave.sil.width
## 1       1  264          0.42
## 2       2   81          0.29

## .
##   1   2 
## 264  81

k = 3 clusters

##   cluster size ave.sil.width
## 1       1  264          0.30
## 2       2   59          0.28
## 3       3   22          0.23

## .
##   1   2   3 
## 264  59  22

k = 4 clusters

##   cluster size ave.sil.width
## 1       1  134          0.14
## 2       2  130          0.25
## 3       3   59          0.18
## 4       4   22          0.23

## .
##   1   2   3   4 
## 134 130  59  22

Final cluster identification

Use DIANA, k = 2

## .
##   1   2 
## 264  81